Bootstrapping non-stationary stochastic volatility

Granular modelling of signals: A framework of Granular Computing

SummaryTo quantify the major environmental drivers of stream bacterial population dynamics, we modelled temporal differences in stream bacterial communities to quantify community shifts, including those relating to cyclical seasonal variation and more sporadic bloom events. We applied Illumina MiSeq 16S rRNA bacterial gene sequencing of 892 stream biofilm samples, collected monthly for 36‐months from six streams. The streams were located a maximum of 118 km apart and drained three different catchment types (forest, urban and rural land uses). We identified repeatable seasonal patterns among bacterial taxa, allowing their separation into three ecological groupings, those following linear, bloom/trough and repeated, seasonal trends. Various physicochemical parameters (light, water and air temperature, pH, dissolved oxygen, nutrients) were linked to temporal community changes. Our models indicate that bloom events and seasonal episodes modify biofilm bacterial populations, suggesting that distinct microbial taxa thrive during these events including non‐cyanobacterial community members. These models could aid in determining how temporal environmental changes affect community assembly and guide the selection of appropriate statistical models to capture future community responses to environmental change.

Copula-Based Dependence Characteriztions and Modeling for Time Series

Forecasting ground-level irradiance over short horizons: Time series, meteorological, and time-varying parameter models

Time series analyses are statistical methods used to assess trends in repeated measurements taken at equally spaced time intervals and their relationships with other trends or events, taking account of the temporal structure of such data. An important aspect of descriptive time series analysis is the choice of model for time series decomposition. This paper examined the challenges in choosing between additive and mixed models in time series decomposition. Most of the existing studies have focused on how to choose between additive and multiplicative models with little or no regards on mixed model. The ultimate objective of this study is therefore, to compare the row, column and overall means and variances of the Buys-Ballot table for additive and mixed models. Table 1 shows that the column variances of Buys-Ballot table is constant for additive model but depends on slope and seasonal effects for mixed model. Results show that seasonal variances of the Buys-Ballot table is constant for additive model and a function of slope and seasonal effects for mixed model. Also, when there is no trend (b=0), the estimates of row, column and overall means are the same for the two models while the estimates of seasonal indices are not the same for both additive and mixed models.

Governments across the world rely on their Customs Administration to provide functions that include border security, intellectual property rights protection, environmental protection, and revenue mobilisation amongst others. Analyzing the trends in revenue being collected from Customs is necessary to direct government policies and decisions. Models that can capture the trends being purported from the nominal (nonreal) tax values with respect to the trade volumes (value) over the period are indispensable. Predominant amongst the existing models are the econometric models (the GDP-based model, the monthly receipts model, and the microsimulation model), which are laborious and sometimes unreliable when studying trends in time series data. In this study, we modelled monthly revenue data obtained from the Ghana Revenue Authority-Customs Division (GRA-CD) for the period January 2010 to December 2019 using two traditional time series models, ARIMA model and ARIMA Error Regression Model (ARIMAX), and two machine learning time series models, Bayesian Structural Time Series (BSTS) model and a Neural Network Autoregression model. The Neural Network Autoregression model of the form NNAR (1, 3) provided the best forecasts with the least Mean Squared Error (MSE) of 53.87 and relatively lower Mean Absolute Percentage Error (MAPE) of 0.08. Generally, the machine learning models (NNAR (1, 3) and BSTS) outperformed the traditional time series models (ARIMA and ARIMAX models). The forecast values from the NNAR (1, 3) indicated a potential decline in revenue and this emphasizes the need for relevant authorities to institute measures to improve revenue generation in the immediate future.

The ice core time series from Vostok Station in Antarctica and the North Greenland Ice Core Project have seasonal variation corresponding to the Milankovitch cycles. After removing these cycles, and interpolating to equal time intervals, stationary time series models are fitted. The series show clear directionality and this feature is modelled by either non-Gaussian errors or non-linear time series models. Threshold autoregressive models are fitted by penalized least squares and compared with non-threshold autoregressive models. Since both ice core time series are reasonably modelled as first order autoregressive series with parameters close to one, directionality will arise from non-symmetric error distributions. However, two regime threshold autoregressive models, of order one and two for Greenland and Vostok, respectively, give an improved match to the observed directionality and a reduced sum of squared residuals. Realizations from the threshold autoregressive models are noticeably different from the non-threshold models. Since the non-threshold models are a restricted case of the threshold models, and the threshold models are a better fit to the observed time series, threshold models should provide more realistic realizations. References C. Chatfield. The Analysis of Time Series: An Introduction . CRC Press, 2004. https://www.crcpress.com/The-Analysis-of-Time-Series-An-Introduction-Sixth-Edition/Chatfield/p/book/9781584883173 A. J. Lawrance. Directionality and reversibility in time series. Int. Stat. Rev. 59(1):67–79, 1991. doi:10.2307/1403575 M. M. Mansor, M. E. Glonek, D. A. Green and A. V. Metcalfe. Threshold autoregressive models for directional time series. In I. Rojas and H. Pomares (Eds.), Time Series Analysis and Forecasting Selected Contributions from the ITISE Conference (ITISE 2015) . pp. 13–25, 2016. doi:10.1007/978-3-319-28725-6 M. M. Mansor, M. E. Glonek, D. A. Green and A. V. Metcalfe. Modelling directionality in stationary geophysical time series. International work-conference on Time Series (ITISE 2015) . http://www.researchgate.net/publication/281835075 M. M. Mansor, D. A. Green and A. V. Metcalfe. Modelling and simulation of directional financial time series. Proceedings of the 21st International Congress on Modelling and Simulation (MODSIM 2015) , pp. 1022–1028, 2015. http://www.mssanz.org.au/modsim2015/E4/mansor.pdf M. M. Mansor, D. A. Green and A. V. Metcalfe. Directionality and volatility in electroencephalogram time series. Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics (ICMSS 2016), AIP Conf. Proc. 1739:020080, 2016. doi:10.1063/1.4952560 North Greenland Ice Core Project members. High-resolution record of Northern Hemisphere climate extending into the last interglacial period. Nature , 431:147–151, 2004. doi:10.1038/nature02805 J. R. Petit, J. Jouzel, D. Raynaud, N. I. Barkov, J.-M. Barnola, I. Basile, M. Bender, J. Chappellaz, M. Davis, G. Delaygue, M. Delmotte, V. M. Kotlyakov, M. Legrand, V. Y. Lipenkov, C. Lorius, L. Pepin, C. Ritz, E. Saltzman and M. Stievenard. Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica. Nature , 399:429–436, 1999. doi:10.1038/20859 S. Soubeyrand, C. E. Morris and E. K. Bigg. Analysis of fragmented time directionality in time series to elucidate feedbacks in climate data. Environ. Modell. Softw. 61:78–86, 2014. doi:10.1016/j.envsoft.2014.07.003

This article presents a study of revenue forecasting in a Florida municipal government. Seven techniques, including the budget officers' judgmental approach, time series models, a deterministic model, and an optimized model, are employed with franchise and utility receipts in the Town of Davie. The authors found that simple time series models outperformed deterministic models and the judgmentally derived forecasts of local officials. Consistent with prior research, findings here suggest that the time series models are not only accurate, but also easy to implement and readily comprehensible by local officials.

Inflation is a constant and consistent increase in the general price level in the country, due to which the purchasing power of a national currency unit decreases. In practice, the measures of inflation are various price indices, such as a consumer price index (CPI), producer price index (PPI), or gross domestic product deflator. However, inflation is usually defined as a change in the HCPI over a year. Time series models, linear regression models and a vector autoregression model (VAR) can be used to model and forecast inflation processes. This paper examines Lithuanian consumer price inflation using a modern stationary time series and econometric theory. The vector autoregression model is proposed for inflation modelling. Theoretical aspects of model estimation are reviewed: time series stationarity, model identification, parameter estimation, model usage and forecasts. The stationarity of the HCPI index and exogenous variables are analyzed using the Augmented Dickey–Fuller (ADF) test. A vector autoregression model of Lithuanian inflation processes is investigated and proposed for inflation modelling. The obtained model is used for forecasting purposes and shows a fairly high degree of accuracy of the inflation forecast in the coming 12-month period.

In modern gas distribution practices, the ability to remotely access operational data and monitor plant conditions in real-time is becoming paramount in assessing operational intricacies. In this study, a robust system that provides real-time access to turbine meter operation data and predicts the time until failure, enhancing maintenance schedules and reducing unexpected downtimes is presented. To achieve this, a comprehensive methodology was employed, starting with the design and development of a real-time data collection system using a Raspberry Pi 4 and various communication components to monitor gas flow parameters being emitted from a simulation software environment. Data collected from the system was then used to train predictive models. Regression models, including Random Forest Regressor, Gradient Boosting Regressor, and Support Vector Regressor, were compared with time-series models like SARIMA. The models were evaluated based on metrics such as Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), and R2. Additionally, anomaly detection models like Isolation Forest were implemented to identify deviations in gas flow data. The results demonstrated that the Random Forest Regressor provided the best result when compared with other regression models used. However, the time-series model, SARIMA slightly outperformed regression techniques, showing a 2.14% reduction in RMSE and a 2.02% increase in R2 at the cost of higher computational demands. The real-time monitoring device achieved high reliability with a latency of 5 seconds and a system reliability of over 95%. These findings underscore the effectiveness of both regression and time-series models in predicting the time until failure of turbine meters. The study provides a framework for predictive maintenance in the gas industry that can minimize operational disruptions and optimize general maintenance practices.

Stochastic versions of chaotic time series: Generalized logistic and Hénon time series models

The application of Big Data and time series models is currently at an early stage. This paper examines the relevance and use of time series analyses for Big Data and business analytics by discussing the emergence of Big Data in business, presenting time series models, and providing an example of how time series models can be efficiently and effectively applied in accounting and auditing using Big Data. Using sophisticated Big Data and time series models, millions of transactions can be searched to spot patterns and detect abnormalities and irregularities. The time series model and Big Data analysis presented in this paper provide policy, practical, educational, and research implications. Businesses and management can use our suggested time series model and Big Data analysis in their predictive models of managerial strategies, decisions, and actions. Business schools and accounting programs can integrate the time series model, Big Data, and data analytics into business and accounting education.

Autoregressive Integrated Moving Average (ARIMA) Box-Jenkins models combine the autoregressive and moving average models to a stationary time series after the appropriate transformation, while the nonlinear autoregressive (N.A.R.) or the autoregressive neural network (ARNN) models are of the kind of multi-layer perceptron (M.L.P.), which compose an input layer, hidden layer and an output layer. Monthly streamflow at the downstream of the Euphrates River (Hindiya Barrage) /Iraq for the period January 2000 to December 2019 was modeled utilizing ARIMA and N.A.R. time series models. The predicted Box-Jenkins model was ARIMA (1,1,0) (0,1,1), while the predicted artificial neural network (N.A.R.) model was (M.L.P. 1-3-1). The results of the study indicate that the traditional Box-Jenkins model was more accurate than the N.A.R. model in modeling the monthly streamflow of the studied case. Performing a one-step-ahead forecast during the year 2019, the forecast accuracy between the forecasted and recorded monthly streamflow for both models was as follows: the Box-Jenkins model gave root mean squared error (RMSE = 48.7) and the coefficient of determination = 0.801), while the (NAR) model gave (RMSE = 93.4) and = 0.269). Future projection of the monthly stream flow through the year 2025, utilizing the Box-Jenkins model, indicated the existence of long-term periodicity.

In time-series analysis, particularly in finance, generalized autoregressive conditional heteroscedasticity (GARCH) models are widely applied statistical tools for modelling volatility clusters (i.e., periods of increased or decreased risk). In contrast, it has not been considered to be of critical importance until now to model spatial dependence in the conditional second moments. Only a few models have been proposed for modelling local clusters of increased risks. In this paper, we introduce a novel spatial GARCH process in a unified spatial and spatiotemporal GARCH framework, which also covers all previously proposed spatial ARCH models, exponential spatial GARCH, and time-series GARCH models. In contrast to previous spatiotemporal and time series models, this spatial GARCH allows for instantaneous spill-overs across all spatial units. For this common modelling framework, estimators are derived based on a non-linear least-squares approach. Eventually, the use of the model is demonstrated by a Monte Carlo simulation study and by an empirical example that focuses on real estate prices from 1995 to 2014 across the postal code areas of Berlin. A spatial autoregressive model is applied to the data to illustrate how locally varying model uncertainties (e.g., due to latent regressors) can be captured by the spatial GARCH-type models.

Machine learning algorithms such as Support Vector Machine (SVM) and Artificial Neural Network (ANN) are used for machine trading. The problem with SVM and ANN is that it is difficult to determine appropriated features for both models; moreover, it is also time consuming to perform backpropagation for ANN when a number of both features and data increase. However, machine trading is not confined only these two algorithms, but also time series models. In this study, we will employ time series models namely Autoregressive Integrated Moving Average (ARIMA) and Holt – Winters’ Exponential Smoothing (HW) as the guidance for trading since time series models only require time series as an input. We will perform time series analysis to snatch the trading opportunity in the Stock Exchange of Thailand (SET). There are fifty companies on the list of SET50 index; we will choose five amongst them to invest measured by Sharpe Ratio; the top five from this measurement will be selected as invested assets in simulated portfolio. Furthermore, the well-known portfolio optimization framework by Harry Markowitz will be used to ensure that the combination of the invested assets is located on the efficient frontier; the result from this study is favorable as the return generated by these activities outperforms market return; furthermore, manipulating time series into different time lags yields higher return and as well as combining both ARIMA and HW models to help predict stock prices also improves power of prediction of time series models. This study will help retail investor who has limited resource overthrow bias and intuition throughout investment decision process ranging from finding the stocks for investment to capturing market movement for trading opportunity.